Preheat oven to 350°F (175°C) and generously grease a 6-cavity donut pan with non-stick cooking spray or coconut oil.
In a large mixing bowl, sift and whisk together the oat flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt until uniform.
In a separate medium bowl, emulsify the egg, maple syrup, applesauce, almond milk, and vanilla extract by whisking vigorously until smooth.
Incorporate the wet mixture into the dry ingredients, stirring with a silicone spatula until no dry streaks remain.
Fold the grated carrots and chopped walnuts into the batter until evenly distributed.
Transfer the batter to a piping bag or large zip-top bag with the corner snipped off, and pipe into the donut cavities until three-quarters full.
Bake for 14 to 16 minutes until the internal temperature reaches approximately 200°F (93°C) or until a toothpick emerges clean.
Remove from oven and allow to stabilize in the pan for 5 minutes before transferring to a wire cooling rack.
Once completely cooled, optionally top with a glaze of 2 oz softened cream cheese mixed with 1 tablespoon of maple syrup.